The world champ's place on the grid next year is still uncertain after his contract talks stalled.
McLaren, who are keen on an all-Brit team of Lewis Hamilton and Button, and Toyota are monitoring things, but time is running out with teams keen to sort out their 2010 driver line-ups.
Key engineering staff at Brawn are understood to be upset by delays in bonus payments.
Button wants to stay with the team but expects his salary to rise by £5million to £8m, having taken a £5m cut this year.
The Frome flier, 29, said: "I'm not that expensive. I want to be with Brawn but I'm going to put some pressure on them."
Brawn would be committed to paying Button if they signed him to a three-year deal, even if they then found they did not have the funds to stay in F1. The team competed this year thanks to a £100m golden goodbye from Honda after the Japanese giant pulled out of the sport last December.
Brawn also signed a deal with Virgin but Richard's Branson's financial commitment was not huge and he is expected to link up with new team Manor F1.
But boss Ross Brawn insisted: "We are positioned well for next year. We will sit down with Jenson and talk about his contract after the final race in Abu Dhabi."
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